That is directly what the manga says. Again, listen to what Hanami said, that sword cannot harm her because it’s not a cursed tool, and cannot keep up with her strength. That’s the exact reason why when Megumi pulls out the black sword, she openly admits it’s a good sword.
Same goes for point two.
Are we not forgetting the Grading system is somewhat flawed? Semi-Grade 1 Mechamaru was absolutely embarrassed by Semi-Grade 2 Base Panda, Second Grade Yuji is stated to be stronger than First Grade Todo, and, literally, Maki Zenin’s existence.
Yes, I am. Do you think that Geto, who was stated to be superior twice, needed an amp to beat a just barely experienced Yuta? Do you think Toji needed to be amped against Dagon?